I think you'll be fine removing the chimney yourself, i have no real construction experience but removed a chimney from my house with relative ease.
Its a messy experience thats for sure, make sure your room is covered in sheets if your going to take this on.
The main thing to remember when removing a chimney is to start at the top! Make sure with every brick you take our that its not supporting anything above it, if you do this you should be fine.
If you are in a terraced house / semi it could also be more difficult as you could be sharing a chimney breast. As i said you need to start at the top, so this HAS to come down first, or it will simply fall through yoru roof, if your breast is attached to your neighbours, this could cause problems, and id speak to someone with a bit more know how.
One are that suprised me when i removed my chimney was that the 1st floor trusses where ties in to the chimnet, i.e the brick of the chimney breast was holding up the trusses. This obviously created a probelm when i removed the supporting bricks, especially at teh time as I had a pile of bricks next to me. I soon got around this problem by bolting some wood on as a splice where the breast was, but its worth keeping in mind!
Hope this helps, if you have any quetsions, just ask!
Al